Toolbox: tox

Toxicokinetics in relation to effects of chemicals on organisms and populations, i.e. on survival, body growth, reproduction, population growth.

The theory for the models can be found in:
Kooijman, S. A. L. M. and Bedaux, J. J. M. 1996. The analysis of aquatic toxicity data. VU University Press, Amsterdam.
Kooijman, S. A. L. M. 2010 Dynamic Energy and Mass Budgets theory for Metabolic Organisation. Cambridge University Press.


tox

Demo that runs:

These files are script-files that illustrate the use of fomort and algatox. Consult these script-files for further explanation.


fomort

Meant to be used as subroutine for scsurv2.
The name of the routine stands for first-order mortality. The function specifies the survival probability of blank individuals, that are exposed to a constant concentration of toxic compound. The toxicokinetics is assumed to be of the first-order type; the hazard rate is assumed to be linear in the internal concentration. Concentrations below the internal no-effect concentration do not affect survival. The proportionality factor with which the hazard rate increases with concentration minus the no-effect concentration is called the killing rate. The hazard rate in the blank is assumed to be constant.

Parameter interpretation:

  1. 1/d, hazard rate in the blank (>0)
  2. M, No-Effect-Concentration
  3. 1/(d*M), killing rate
  4. 1/d, elimination rate

An example of application of fomort in regression and plotting routines is given in the script-file mydata_fomort.


fomort_c0

Meant to be used as subroutine for scsurv2.
Like fomort, but the no effect concentrations follows a log normal distribution.

Parameter interpretation:

  1. 1/d, hazard rate in the blank (>0)
  2. M, No-Effect-Concentration
  3. 1/(d*M), killing rate
  4. 1/d, elimination rate
  5. -, scatter parameter for the No-Effect-Concentration

The use is similar to fomort.


fomortph

Meant to be used as subroutine for scsurv2.
The name of the routine stands for first-order mortality with effects on pH. The model is identical to fomort, except that the NEC and the killing rates depend on the pH, because the these parameters differ for the molecular and the ionic form.

Parameter interpretation:

  1. 1/d, hazard rate in the blank
  2. M, No-Effect-Concentration of molecular form
  3. 1/(d*M), killing rate of molecular form
  4. 1/d, elimination rate
  5. M, No-Effect-Concentration of ionic form
  6. 1/(d*M), killing rate of ionic form
  7. -, ion-product constant

An example of application of fomortph in regression and plotting routines is given in the script-file mydata_fomortph. Notice that this model does not specify a response surface; thus shsurv2 only works properly with option 'plotnr' = 1.


lfohaz

Calculates the minus log-likelihood function for first-order mortality, if time-to-death data are available for each individual. The model is otherwise the same as in fomort. The toxicokinetics is assumed to be of the first-order type; the hazard rate is assumed to be linear in the internal concentration. Concentrations below the internal no-effect concentration do not affect survival. The proportionality factor with which the hazard rate increases with concentration minus the no-effect concentration is called the killing rate. The hazard rate in the blank is assumed to be constant.

Input:

Output:

An example of application of lfohaz in combination with nmmin is given in the script-file mydata_fohaz.


fomort2

Meant to be used as subroutine for scsurv2.
The name of the routine stands for first-order mortality with a mixture of 2 compounds. The function specifies the survival probability of blank individuals, that are exposed to a constant concentration of toxic compound. The toxicokinetics is assumed to be of the first-order type; the hazard rate is assumed to be linear in the internal concentration. The compounds compete for capacity to cancel effects. The effective part, that exceeds to cancel capacity can interact at a rate that can be negetive, zero (independent action), or positive. See further fomort.

Parameter interpretation:

  1. 1/d, hazard rate in the blank (>0)
  2. M, No-Effect-Concentration for compound A
  3. M, No-Effect-Concentration for compound B
  4. 1/(d*M), killing rate for compound A
  5. 1/(d*M), killing rate for compound B
  6. 1/d, elimination rate for compound A
  7. 1/d, elimination rate for compound B
  8. 1/(d*M*M), interaction rate between A and B

An example of application of fomort in regression and plotting routines is given in the script-file mydata_fomort2.


algatox

Routine that specifies a model for effects on nutrient-limited alga growth, with three modes of action: Instantaneous equilibrium is assumed for the internal concentration. Growth is assumed to be nutrient limited, and the nutrient pool is exchanging with a pool that is not available to the algae. Algal mass is measured in Optical Densities. The contribution of living biomass, dead biomass and ghost biomass might differ. The toxic compound can tranfer living into dead biomass, the dead biomass decays to ghost biomass according to a first order process. The no-effect-conc for the three effects are taken to be the same, but they might actually be different, however!

Input:

Output:

An example of application of fomort in regression and plotting routines is given in the script-file mydata_algatox.


lcx & lc50 & lc503

Calculates LC50 and lcx values, given values for the NEC, killing rate and elimination rate.

Input:

Output:

An example of application of lc50: lc50([1, 1, 1], [3 4]), which results in a 2-vector with [LC50.3d LC50.4d]. Another application in regression and plotting routines is given in the script-file mydata_lc50, where LC50 data are used to extract the toxicity parameters (so just opposite to the previous application). Consult the script-file for further explanation. See also lc503.

lc503 calculates values for the NEC, killing rate and elimination rate given three LC50 values.

Input:

Output:

An example of application of lc503 is for an appropriate (3,2) matrix tc: [p, err] = lc503(tc, [1, 1, .1]). The effect is very similar to p = nmregr("lc50", [1, 1, .1]', tc), but lc503 is much faster and exact.


ecx

Calculates ecx values, given parameter values. It uses a symplex method, so the conversion is slow.

Input:

Output:

An example of application: ecx('marep', [.13 1 .16 15 .1 .13 .42 1]', 21, .99), which results in the EC99.21d for effects on reproduction via effects on maintenance.


acc

Calculates internal concentrations, given the elimination rate and BioConcentration Factor (BCF) given exposure to a constant external concentration of a compound. The initial internal concentration is assumed to be nil.

Input:

Output:

An example of application of acc is given in mydata_acc for fitting accumulation data. See also acceli for the case of accumulation and elimination data.


acceli

Calculates internal concentrations, given the elimination rate and BioConcentration Factor (BCF) given exposure to a constant external concentration of a compound, followed by an elimination in absence of the compound. The initial internal concentration is assumed to be nil.

Input:

Output:

An example of application of acceli is given in mydata_acceli for fitting accumulation/elimination data. See also acc for the case of accumulation data only.


*growth

Calculates body lengths during exposure to a constant external concentration of a compound, given parameter values. The initial internal concentration is assumed to be nill and food availability abundant. Toxico-kinetics is assumed to follow the one-compartment model, but dilution by growth is taken into account. No elimination via reproduction is assumed. The internal concentration and the reserve are treated as hidden variables.

These functions are meant to be used via parameter estimation procedures nrregr2, nmregr2 or garegr2. The optional second column of the initial parameter matrix should be used, where most, if not all, of the physiological parameters are fixed (corresponding to value zero in the second column), because toxicity assays hardly contain information about these parameters. In the cases of slow and fast kinetics, the third parameter, the elimination rate, should be kept fixed as well.

Three cases for elimination rates can be chosen and three modes of action, which gives 9 combinations:

  1. slow kinetics: * stands for
  2. normal kinetics: * stands for
  3. fast kinetics: * stands for

Input:

Output:

An example of application of *growth is given in mydata_growth for fitting length data.


*rep

Calculates cumulative number of offspring per female during exposure to a constant external concentration of a compound, given parameter values. The initial internal concentration is assumed to be nill and food availability abundant. Toxico-kinetics is assumed to follow the one-compartment model, but dilution by growth is taken into account. No elimination via reproduction is assumed. The internal concentration, maturity, reserve and structure are treated as hidden variables. The parameters of the embryo are assumed to be affected by the compound in the same way as in the mother; the relevance is in the amount of reserve that is required per egg. The reproduction buffer is assumed to have capacity zero.

These functions are meant to be used via parameter estimation procedures nrregr2, nmregr2 or garegr2. The optional second column of the initial parameter matrix should be used, where most, if not all, of the physiological parameters are fixed (corresponding to value zero in the second column), because toxicity assays hardly contain information about these parameters. In the cases of slow and fast kinetics, the third parameter, the elimination rate, should be kept fixed as well.

Three cases for elimination rates can be chosen and five modes of action, which gives 15 combinations:

  1. slow kinetics: * stands for
  2. normal kinetics: * stands for
  3. fast kinetics: * stands for

Input:

Output:

An example of application of *rep is given in mydata_rep for fitting length data.


*pop

Calculates (microbial) population size during exposure to a constant external concentration of a compound, given parameter values. The internal concentration is assumed to be equilibrium instantaneously.

Input:

* stands for

The adaptiation model is basically the same as the hazard model, but only during the first time increment; the survivors are no longer affected by the compound and the overall effect is a delay of growth only.

Output:

An example of application of *pop is given in mydata_pop for fitting population growth data.


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